Magnetic and inductive components and devices such as coils, inductors, transformers, motors and others (referred to herein as magnetic components) include a winding of one or more of a variety of conductors. Such magnetic components utilize a variety of conductor types including round, square, or rectangular wire; thin conductor strips or foil; multiple wires twisted together or wound in parallel; various Litz or woven magnet wire braids (to increase uniformity of current sharing between elementary conductors); and various combinations of such conductor types.
Conventional solenoidal magnetic components comprise winding layers which form cylinders around a core. In contrast, planar magnetic components utilize conductors and combinations of conductors in an annular configuration. Round, square or rectangular wire, for example, may be wound in annular configurations. In addition, thin conductor strips or foil may be implemented in annular configurations using printed circuit boards, flex circuits, or discrete conductors fabricated from sheet stock, for example, and in other configurations known to those skilled in the art. In comparison to solenoidal magnetic components, the thickness of winding layers and the number of turns per layer in planar magnetic components, such as those on printed circuit boards, may be varied easily and inexpensively.
FIG. 1 illustrates a cross-section of a winding region or portion in a typical magnetic component having n layers. In FIG. 1, the winding length of each layer is designated l. The thickness of each winding layer is designated T1 through Tn and each layer has Ni turns, designated N1 through Nn. The magnetic surface field intensities at the inner and outer boundaries of the ith winding layer are designated as Hi-1 and Hi respectively. The current in the ith winding is designated Ii and points out of the plane of the paper. When the winding length l is much greater than the winding layer thickness, the magnetic field distribution is largely parallel to the plane of the conductor in each winding layer. The magnitude ratio of peak magnetic surface field intensities for each conductor layer is defined as follows: Rn=Hn/Hn-1 for each of n layers. Phase shift or phase displacement of magnetic surface field intensities for each conductor layer is defined as: Φn=φn−φn-1. The turns in FIG. 1 are illustrated by way of vertical lines in each of the winding layers.
Unless otherwise stated, the following additional definitions with implied units are used herein:
                            ⁢                  H          ⁢                      :                    ⁢                                          ⁢          Magnetic          ⁢                                          ⁢          Field          ⁢                                          ⁢          Intensity          ⁢                      :                    ⁢                                          ⁢          units          ⁢                                          ⁢          of          ⁢                                          ⁢                                    Ampere              -              Turn                        Meter                                                          ⁢                              ρ            ⁢                          :                        ⁢                                                  ⁢            Resistivity            ⁢                          :                        ⁢                                                  ⁢            units            ⁢                                                  ⁢            of            ⁢                                                  ⁢            ohm                    -          meter                                                ⁢                                            μ              0                        ⁢                          :                        ⁢                                                  ⁢            Permeability            ⁢                                                  ⁢            constant                    =                      4            ⁢            π            ×                          10                              -                7                                      ⁢                          Henry              Meter                                                                      ⁢                  f          ⁢                      :                    ⁢                                          ⁢          Excitation          ⁢                                          ⁢          frequency          ⁢                      :                    ⁢                                          ⁢          units          ⁢                                          ⁢          of          ⁢                                          ⁢          Hertz                                                ⁢                              δ            ⁢                          :                        ⁢                                                  ⁢            Skin            ⁢                                                  ⁢            Depth                    =                                    ρ                              π                ⁢                                                                  ⁢                                  μ                  0                                ⁢                f                                                        
Magnetic components always incur some power dissipation in the winding(s) and core, which decreases efficiency and increases temperature. It is generally known that alternating current (AC) conduction generates eddy currents within the conductors of magnetic components. Such eddy currents are significant at high frequencies and/or for large conductor thicknesses. These eddy currents do not contribute to the macroscopic current of the device, but produce a field which tends to cancel the external magnetic field produced by the AC current. However, the resultant power dissipation, or loss, and energy storage associated with such eddy currents can have a significant impact on the performance of a magnetic component in an electrical circuit. In particular, dissipation from eddy currents can markedly reduce the electrical efficiency of a system and increase the temperature rise of the component. This is due to the well known skin and proximity effects.
Skin effect is the tendency of the current density in a wire to increase at and near the surface of the wire. In other words, skin effect is the tendency of current in a conductor to flow more toward the surface of the conductor as frequency is increased. Current density decays exponentially inside the conductor, reaching a value at the skin depth (δ) of 1/e times the current density at the surface.
Proximity effect occurs when one conductor is placed in an external field generated by one or more other conductors in close proximity. In that case, eddy currents are induced in the conductor which oppose the penetration of the external field. The two eddy current effects occur simultaneously in a conductor carrying an AC current when the conductor is exposed to an external magnetic field. Such eddy currents cause power dissipation in the windings of magnetic components which increase with frequency and/or at large conductor thicknesses.
Heretofore, designers of wound magnetic components have utilized analytical methods to limit or reduce power dissipation based upon mathematical derivations by P. L. Dowell in 1966 (P. L. Dowell, “Effects of Eddy Currents in Transformer Windings,” Proceedings of the IEEE, Vol. 113, No. 8, August 1966 [incorporated herein by reference]). P. L. Dowell, as with most prior art, assumes a constant layer thickness or height and does not consider current phase displacement.
High frequency analysis of coil regions has been analyzed using a classical equivalent foil representation of a winding layer. This approach facilitates an understanding of physics and determination of conductor boundary conditions. However, this method neglects stray field effects at edges and other asymmetries. Indeed, stray effects can also arise from unpredictable manufacturing variables such as insulation build up and winding terminations which can cause irregular conductor geometries.
Increased computing power has facilitated iterative approaches to determine winding configurations that yield acceptable dissipation. For example, Finite Element Analysis has improved mathematical consideration of asymmetries and specific device geometries. Finite Element Analysis is frequently used to determine whether a specific component design is acceptable. It is less valuable, however, in generating or suggesting all potential design parameters and determining an optimal or desired solution. Finite Element Analysis software may examine the impact of various configuration parameters such as core type, conductor type and size and the configuration of terms without the need to build and test a physical device.
Prior to the present invention, the minimum loss configurations for the individual winding layers of a magnetic component having more than one layer was not analytically derived for the general case. M. P. Perry, “Multiple Layer Series Connected Winding Design for Minimal Losses,” IEEE Transactions on Power Apparatus and Systems, Vol. PAS-98, No. 1, January/February 1979, pp. 116-123, discloses an analysis for minimized power dissipation by choosing specific radial thicknesses for each winding layer in a magnetic component. M. P. Perry's analysis is based on general field solutions for current density distributions in winding layers of an infinitely long, cylindrical current sheet. Also, Perry's analysis assumes a fixed number of turns per layer and zero phase displacement. The analysis, therefore, has limited applicability. In addition, the stated twelve percent reduction in power dissipation in the M. P. Perry paper has subsequently been considered too small a benefit when increased manufacturing costs are considered.
Since prior art methods have focused on the equivalent AC resistance of a complete winding portion or region, the optimization or minimization of loss in discrete winding layers within a magnetic component has not been implemented. As a result, configurations of minimum winding dissipation have been elusive and magnetic components have been less efficient and larger or hotter in comparison to results for an optimized configuration.
U.S. Pat. Nos. 6,455,971 and 6,758,430 (Palma et al.) disclose a non-random winding technique to reduce proximity losses in motors and other electric machines. U.S. Pat. No. 6,617,665 (Farcy et al.) discloses an optimized width for inductive windings on an integrated circuit, the width being twice the “skin thickness” corresponding to the maximum frequency of a high frequency current running through the winding. U.S. Pat. No. 6,650,217 (Wolf et al.) discloses a low profile planar magnetic component having a stacked winding configuration and specifying a minimum distance between winding layers and an air gap. U.S. Pat. No. 6,661,326 (Yeh et al.) discloses a wire-winding structure and method to improve transformer power which consists of a method of winding wire from a pin on a bobbin around a plurality of slots. U.S. Pat. No. 6,536,701 (Fulton et al.) discloses the use of an improved former for winding electrical coils. None of these patents discloses a device or method having improved winding parameters as in the present invention.
Generally, the prior art assumes uniform conductor thickness; approximates dissipation in terms of an equivalent AC/DC resistance ratio for the entire winding portion; and suggests that the best way to reduce winding eddy current loss in a magnetic component is to reduce the number of layers. In addition, none of the prior art accounts for phase displacement in determining preferred winding parameters.
There is a need, therefore, for an improved magnetic component having desired or optimal winding parameters including winding layer thickness, number of winding layers and considering variable turns per winding layer. There is also a need for a cost-effective method of designing and/or manufacturing such magnetic components to reduce power dissipation. Since multiple transformer secondaries, for example, can have loads with unequal power factors, or differing nonlinear loads (e.g. independent secondary regulators), and since significant magnetization currents can occur in primary windings, the harmonic components of winding currents can have significant relative phase displacement. It is desirable, therefore, to provide a single method of designing or calculating winding parameters which may be applied to general boundary conditions, including consideration for relative phase displacement of winding currents.